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We study the online constrained ranking problem motivated by an applicationto web-traffic shaping: an online stream of sessions arrive in which, withineach session, we are asked to rank items. The challenge involves optimizing theranking in each session so that local vs. global objectives are controlled:within each session one wishes to maximize a reward (local) while satisfyingcertain constraints over the entire set of sessions (global). A typicalapplication of this setup is that of page optimization in a web portal. We wishto rank items so that not only is user engagement maximized in each session,but also other business constraints (such as the number of views/clicksdelivered to various publishing partners) are satisfied.  We describe an online algorithm for performing this optimization. A novelelement of our approach is the use of linear programming duality andconnections to the celebrated Hungarian algorithm. This framework enables us todetermine a set of \emph{shadow prices} for each traffic-shaping constraintthat can then be used directly in the final ranking function to assignnear-optimal rankings. The (dual) linear program can be solved off-lineperiodically to determine the prices. At serving time these prices are used asweights to compute weighted rank-scores for the items, and the simplicity ofthe approach facilitates scalability to web applications. We provide rigoroustheoretical guarantees for the performance of our online algorithm and validateour approach using numerical experiments on real web-traffic data from aprominent internet portal.

Online Ranking with Constraints: A Primal-Dual Algorithm and Applications to Web Traffic-Shaping